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QUARTZ CRYSTALS
Synthetic quartz is composed of Silicon and Oxygen (Silicon
Dioxide) and is cultured in autoclaves under high pressure and
temperature. Quartz exhibits piezoelectric properties which
generate an electrical potential when pressure is applied on
the surfaces of the crystal. Conversely, when an electrical
potential is applied to the surfaces of a crystal, mechanical
deformation or vibration is generated. These vibrations occur
at a frequency determined by the crystal design and oscillator
circuit. Under proper conditions, quartz can be used to
stabilize the frequency of an oscillator circuit.
CENTER FREQUENCY
The specified reference frequency of the crystal and is
typically specified in megahertz (MHz) or kilohertz (kHz).
FREQUENCY TOLERANCE OR CALIBRATION ACCURACY
The amount of frequency deviation from a specified center
frequency at ambient temperature (referenced at 25°C).
This parameter is specified with a maximum and minimum
frequency deviation, expressed in percent (%) or parts per
million (ppm). This deviation is associated with a set of
operating conditions including: Load Capacitance and Drive
Level.
FREQUENCY STABILITY
The amount of frequency deviation from the ambient
temperature frequency over the operating temperature range.
This deviation is associated with a set of operating conditions
including: Operating Temperature Range, Load Capacitance,
and Drive Level. This parameter is specified with a maximum
and minimum frequency deviation, expressed in percent
(%) or parts per million (ppm). The frequency stability is
determined by the following primary factors: Type of quartz
cut and angle of the quartz cut. Some of the secondary factors
include: mode of operation, drive level, load capacitance,
and mechanical design.
TYPE/ANGLE OF QUARTZ CUT
The type and angle of a quartz cut effects the crystal device
operating parameters, the most significant being frequency
stability. The frequency stability is dependant upon the
plane or the angle of the crystal element in relation to the
crystalline axes of the crystal. The plane or angle is referred
to as the crystal "cut". As shown in Figure 1, a common type
of thickness shear crystal fabricated from Y bar quartz is the
"AT" cut. In Figure 2, the frequency stability versus operating
temperature range is plotted as a function of "AT" cut angle
(0). Note the inflection point at approximately 25°C and
the location of the adjacent upper and lower turning points
for each cut angle. The frequency stability and operating
temperature range required by the customer determine the
angle of cut utilized.
OPERATING TEMPERATURE RANGE
The maximum and minimum temperatures that the crystal
device can be exposed to during oscillation. Over this
temperature range, all of the specified device operating
parameters are guaranteed.
CRYSTAL EQUIVALENT CIRCUIT
A crystal device consists of a quartz resonator with metal
plating. This plating, as shown in Figure 3, is located on
both sides of the crystal and is connected to insulated leads
on the crystal package. The device exhibits a piezoelectric
response between the two crystal electrodes as expressed in
the equivalent circuit shown in Figure 4.
MOTIONAL CAPACITANCE (C1)AND MOTIONAL INDUCTANCE (L1)
The motional capacitance and inductance are designated by
C1 and L1, respectively, in the equivalent circuit (Figure 4).
For a "Series" resonant crystal, the value of C1 resonates with
the value of L1 at a frequency (FS) expressed in Equation
1. Typically, L1 is not mentioned when working with most
crystals. Due to this absolute equation, it is only necessary
to specify one motional component or the other. The industry
standard is to specify a proper value of C1 only. The actual
value of C1 has physical limitations when it is realized in a
quartz crystal design. These constraints include the mode of
operation, the quartz cut, the mechanical design, and the
nominalf requency of the crystal.
SHUNT CAPACITANCE (C0)
The static capacitance between the crystal terminals. Measured
in picofarads (pF), Shunt Capacitance is present whether the
device is oscillating or not (unrelated to the piezoelectric
effect of the quartz). Shunt Capacitance is derived from the
dielectric of the quartz, the area of the crystal electrodes,
and the capacitance presented by the crystal holder.
EQUIVALENT SERIES RESISTANCE (ESR)
The resistive element, measured in ohms, of a crystal device.
At the frequency found in Equation 1, the motional inductance
(L1) and motional capacitance (C1) are of equal ohmic value
but are exactly opposite in phase. The net result is that
they cancel one another and only a resistance remains in
the series leg of the equivalent circuit (Figure 4).
The ESR measurement is made only at the series resonant
frequency (FS), not at some predetermined parallel resonant
frequency (FL). Crystal resistance measured at some parallel
load resonant frequency is often called the "effective"
resistance.
SERIES VS. PARALLEL LOAD RESONANCE
A crystal can be used in an oscillator circuit to operate
in either of two resonant modes: Series Resonance
or Parallel Load Resonance (also known as anti-resonance).
The crystals used in these two types of
modes are physically the same crystal, but are calibrated
to slightly different frequencies. The crystal reactance
curve is shown in Figure 5. When a crystal is placed
into an oscillator circuit, they oscillate together at a
tuned frequency. This frequency is dependent upon the
crystal design and the amount of Load Capacitance,
if any, the oscillator circuit presents to the crystal.
Specified in picofarads (pF), Load Capacitance is
comprised of a combination of the circuits discrete load
capacitance, stray board capacitance, and capacitance
from semiconductor miller effects. When an oscillator
circuit presents some amount of load capacitance to a
crystal, the crystal is termed "Parallel Load Resonant",
and a value of Load Capacitance must be specified.
If the circuit does not exhibit any capacitive loading,
the crystal is termed "Series Resonant", and no value
of Load Capacitance is specified. The "Parallel Load
Resonant" operating frequency of a quartz crystal is
based on Equation 2.
MODE OF OPERATION
The Mode of Operation of a quartz device is one
of the factors that will determine the frequency of
oscillation. For "AT" cut quartz crystals, over tone
modes are at odd frequency harmonics. For example,
a crystal may operate at its fundamental frequency
of 10 MHz, or at odd harmonics of approximately
30MHz (Third Overtone), 50MHz (Fifth Overtone), and
70 MHz (Seventh Overtone). The equivalent circuit of
an overtone mode is not shown in the above model
(Figure 4), but each over tone mode would simply be
an additional parallel R1, L1, C1 branch (no additional
C0 branches) equivalent to the fundamental circuit
shown.
DRIVE LEVEL
A function of the driving or excitation current flowing
through the crystal. The Drive Level is the amount
of power dissipation in the crystal, expressed in
microwatts or milliwatts. Maximum power is the most
power the device can dissipate while still maintaining
operation with all electrical parameters guaranteed.
Drive level should be maintained at the minimum levels
necessary to initiate proper start-up and assure steady
state oscillation. Excessive drive level can cause poor
aging characteristics and crystal damage.
AGING
The systematic change in frequency with time due to
internal changes in the crystal and/or oscillator. Aging is
often expressed as a maximum value in parts per million
per year [ppm/year]. The rate of aging is typically greatest
during the first 30 to 60 days after which time the
aging rate decreases. The following factors effect crystal
aging: adsorption and desorption of contamination on
the surfaces of the quartz, stress relief of the mounting
and bonding structures, material outgassing, and seal
integrity.
STORAGE TEMPERATURE RANGE
The minimum and maximum temperatures that the device
can be stored or exposed to when in a non-oscillation
state. After exposing or storing the device at the minimum
or maximum temperatures for a length of time, all of
the operating specifications are guaranteed over the
specified Operating Temperature Range.
PULLABILITY
A specification for the change in the parallel load
resonant frequency as a function of change in crystal
load capacitance. As expressed graphically in Figure 6,
Equation 3 is used to calculate the frequency
difference, expressed in ppm, between two parallel load
resonant frequencies (FCL1 and FCL2) as a direct result
of a given change in crystal load capacitance (CL1 and
CL2). Because there are several methods to express
crystal pullability, please consult the factory for product
specifications.
CAPACITIVE RATIO
In applications (i.e. VCXO) where variations in the crystal
parallel resonant frequency are desired, the capacitive
ratio (r) may be specified. Derived from Equation 1
and rearranged, the capacitive ratio is a component of
Equation 4. This ratio is an indicator of the change
in a parallel load resonant frequency as a direct result
of a given change in crystal load capacitance. Because
the value of this ratio has physical limitations when it
is realized in a quartz crystal design, please consult the
factory for product specifications.
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